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94 CHAPTER 2

5. J. O’M. Bockris and J. Bowler-Reed, “A Technique for Measuring Dielectric Constants
in Conducting Solution,” J. Appl. Phys. 2: 74 (1951).
Papers
1. D. Bertolini, M. Cassetari, E. Tombari, and S. Verenesi, Rev. Sci. Instrum. 61: 450 (1990).
2. R. S. Drago, D. C. Feris, and N. Wong, J. Am. Chem. Soc. 112: 8953 (1990).
3. S. Safe, R. K. Mohr, C. J. Montrose, and T. A. Litovitz, Biopolymers 31: 1171 (1991).
4. M. Bruehl and J. T. Hynes, J. Phys. Chem. 96: 4068 (1992).
5. J. Z. Bao, M. L. Swicord, and C. C. Davis, J. Chem. Phys. 104: 4441 (1996).
6. J. L. Buck, IEEE Transactions 45: 84 (1996).

2.13. IONIC HYDRATION IN THE GAS PHASE

Now that some methods for investigating the structure of the ion–solvent complex
in solution have been described, it is time to learn systematically what is known about
it. One can start by considering systems that avoid the complexity of liquid water. By
varying the partial pressure of water vapor while keeping it low (0.1–10kPa), it is possible
to find the equilibrium constant between water vapor and the entities represented by a
number of ion–solvent aggregates, in the gas phase (Kebarle and Godbole,
1968).
Thus, if the equilibrium constant K for one of these equilibria is known, can
be derived from the well-known thermodynamic relation If K
(and hence ) is known as a function of T, can be obtained from the slope of
an In and from the intercept.
The seminal work in this field was carried out by Kebarle and it is surprising to
note the gap of 30 years between the foundation paper by Bernal and Fowler on solvation
in solution and the first examination of the simpler process of hydration in the gas phase.
A series of plots showing the concentrations of various hydrate complexes for
as a function of the total pressure of water vapor is given in Fig. 2.29. 26
Now, an interesting thing can be done with the values obtained as indicated
earlier. One takes the best estimate available for the primary hydration number in
solution (see, e.g., Tables 2.7 and 2.11). One then calculates the corresponding heat
of hydration in the gas phase for this number and compares it with the corresponding
individual heat of hydration of the ion in solution. The difference should give the
residual amount of interaction heat outside the first layer (because in the gas phase
there is no “outside the first layer”).
The hydration energy for the outer shell turns out to be 15% of the whole for
cations and about 30% for anions. Thus, in hydration of the alkali and halide ions,

26
In Fig. 2.29 a non-SI unit, the torr, is used. The unit is named for Torricelli, who first discussed the partial
vacuum above mercury contained in a tube and found it to be of an atmosphere.